The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a height of 6 units, and the right cylinder has a height of 4 units. Which conclusion can be made from the given information?Group of answer choicesThe volume of the triangular prism is half the volume of the cylinder.The volume of the triangular prism is twice the volume of the cylinder.The volume of the triangular prism is equal to the volume of the cylinder.The volume of the triangular prism is not equal to the volume of the cylinder.
Question
The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a height of 6 units, and the right cylinder has a height of 4 units. Which conclusion can be made from the given information?Group of answer choicesThe volume of the triangular prism is half the volume of the cylinder.The volume of the triangular prism is twice the volume of the cylinder.The volume of the triangular prism is equal to the volume of the cylinder.The volume of the triangular prism is not equal to the volume of the cylinder.
Solution
The volume of a shape is calculated by multiplying the cross-sectional area by the height. In this case, both the triangular prism and the cylinder have the same cross-sectional area, but different heights.
The volume of the triangular prism would be the cross-sectional area times the height of 6 units. The volume of the cylinder would be the cross-sectional area times the height of 4 units.
Since the cross-sectional area is the same for both shapes, the shape with the greater height will have the greater volume. Therefore, the volume of the triangular prism is greater than the volume of the cylinder.
So, the correct answer is: The volume of the triangular prism is not equal to the volume of the cylinder.
Similar Questions
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 628 square units, and the area of the cross-section of the cylinder is 200π square units. Based on this information, which argument can be made?Group of answer choicesThe volume of the square prism is the volume of the cylinder.The volume of the square prism is half the volume of the cylinder.The volume of the square prism is equal to the volume of the cylinder.The volume of the square prism is twice the volume of the cylinder.
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